CAIIB Formula Sheet
Ten formulas, what each one is for, and a worked example.
CAIIB's numerical questions come from three papers. ABM covers statistics, BFM covers risk management and treasury, and ABFM covers capital budgeting. The formulas below are the ones that turn up across all three.
Each comes with a one-line note on where it's used, followed by a worked expected-loss example.
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The 10 Formulas
1
Formula
Arithmetic mean
Expression
x̄ = Σx ÷ n
Use it for
Average of a data set (ABM statistics).
2
Formula
Standard deviation
Expression
σ = √[Σ(x − x̄)² ÷ n]
Use it for
How spread out the values are; the base of most risk measures.
3
Formula
Coefficient of variation
Expression
CV = (σ ÷ x̄) × 100
Use it for
Comparing the variability of two series with different averages.
4
Formula
Correlation coefficient
Expression
r = Cov(X, Y) ÷ (σₓ × σᵧ)
Use it for
Strength of the linear link between two variables, from −1 to +1.
5
Formula
Macaulay duration
Expression
D = Σ[t × PV(CFₜ)] ÷ Bond price
Use it for
Weighted average time to a bond's cash flows (BFM).
6
Formula
Modified duration and price change
Expression
MD = D ÷ (1 + y); ΔP ≈ −MD × Δy × P
Use it for
Estimating how much a bond's price moves when yields change.
7
Formula
Value at Risk (parametric)
Expression
VaR = Position × z × σ × √t
Use it for
Maximum expected loss at a confidence level over t days.
8
Formula
Expected loss
Expression
EL = PD × LGD × EAD
Use it for
Credit risk provisioning and pricing.
9
Formula
Capital adequacy ratio
Expression
CRAR = Eligible capital ÷ Risk-weighted assets × 100
Use it for
Basel III capital requirement for banks.
10
Formula
Net present value
Expression
NPV = Σ CFₜ ÷ (1 + k)ᵗ − Initial investment
Use it for
Accept or reject a project in capital budgeting (ABFM).
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Arithmetic mean | x̄ = Σx ÷ n | Average of a data set (ABM statistics). |
| 2 | Standard deviation | σ = √[Σ(x − x̄)² ÷ n] | How spread out the values are; the base of most risk measures. |
| 3 | Coefficient of variation | CV = (σ ÷ x̄) × 100 | Comparing the variability of two series with different averages. |
| 4 | Correlation coefficient | r = Cov(X, Y) ÷ (σₓ × σᵧ) | Strength of the linear link between two variables, from −1 to +1. |
| 5 | Macaulay duration | D = Σ[t × PV(CFₜ)] ÷ Bond price | Weighted average time to a bond's cash flows (BFM). |
| 6 | Modified duration and price change | MD = D ÷ (1 + y); ΔP ≈ −MD × Δy × P | Estimating how much a bond's price moves when yields change. |
| 7 | Value at Risk (parametric) | VaR = Position × z × σ × √t | Maximum expected loss at a confidence level over t days. |
| 8 | Expected loss | EL = PD × LGD × EAD | Credit risk provisioning and pricing. |
| 9 | Capital adequacy ratio | CRAR = Eligible capital ÷ Risk-weighted assets × 100 | Basel III capital requirement for banks. |
| 10 | Net present value | NPV = Σ CFₜ ÷ (1 + k)ᵗ − Initial investment | Accept or reject a project in capital budgeting (ABFM). |
What the Symbols Mean
- PD, LGD, EAD
- Probability of default, loss given default and exposure at default.
- y
- Yield per period. Use the semi-annual yield for semi-annual coupons.
- z
- The confidence-level multiplier: 1.65 for 95% and 2.33 for 99%, one-tailed.
- k
- Discount rate, usually the cost of capital.
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Worked Example: Expected Loss on a Loan
A ₹10,00,000 exposure with a 2% probability of default and 45% loss given default.
- 1
Write down the inputs
EAD = ₹10,00,000. PD = 0.02. LGD = 0.45.
- 2
Multiply them
EL = 0.02 × 0.45 × 10,00,000 = ₹9,000.
- 3
Read the answer
On average the bank expects to lose ₹9,000 a year on this loan, which it covers through pricing and provisions.
Duration Questions Hide the Compounding
For a bond paying semi-annual coupons, divide the yield by 2 when you convert Macaulay duration to modified duration. Many options in duration questions are built on forgetting this step.
FAQs
Which CAIIB papers are numerical?expand_more
ABM (statistics and quantitative techniques), BFM (risk management and treasury) and parts of ABFM (capital budgeting). BRBL is almost entirely law and regulation.
Are z-values given in the CAIIB exam?expand_more
Questions usually state the confidence level. It's safest to remember 1.65 for 95% and 2.33 for 99%.
Is CRAR calculated on total assets?expand_more
No. CRAR is capital divided by risk-weighted assets, not total assets.
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